Eric Ryan/Getty Images(LOS ANGELES) -- Kanye West and Kim Kardashian have yet to share any pictures of their new daughter, North, since her arrival June 15, and it’s unlikely we’ll see anything in the foreseeable future. The couple has reportedly turned down a $3 million offer from an Australian magazine.

A source tells Us Weekly magazine that West has been "adamant" about not having the baby appear on Kardashian’s reality show, Keeping Up with the Kardashians.

“He was serious when he said North isn’t America’s baby, so he may not do anything,” the source says.

The 36-year-old rapper’s protective instincts go beyond ensuring North’s privacy. The source describes West as being a doting father and a “super worrywart” over her, staying by her side as much as possible.

A friend of West’s tells Us, “Kim told him it was good to get out. He couldn’t wait to get back. North is all they talk about.”